Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 582-586
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V. D. Antopol'skii. On a condition for twofold transitivity of a primitive group of permutations. Sbornik. Mathematics, Tome 14 (1971) no. 4, pp. 582-586. http://geodesic.mathdoc.fr/item/SM_1971_14_4_a7/
@article{SM_1971_14_4_a7,
author = {V. D. Antopol'skii},
title = {On a~condition for twofold transitivity of a~primitive group of permutations},
journal = {Sbornik. Mathematics},
pages = {582--586},
year = {1971},
volume = {14},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_14_4_a7/}
}
TY - JOUR
AU - V. D. Antopol'skii
TI - On a condition for twofold transitivity of a primitive group of permutations
JO - Sbornik. Mathematics
PY - 1971
SP - 582
EP - 586
VL - 14
IS - 4
UR - http://geodesic.mathdoc.fr/item/SM_1971_14_4_a7/
LA - en
ID - SM_1971_14_4_a7
ER -
%0 Journal Article
%A V. D. Antopol'skii
%T On a condition for twofold transitivity of a primitive group of permutations
%J Sbornik. Mathematics
%D 1971
%P 582-586
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1971_14_4_a7/
%G en
%F SM_1971_14_4_a7
The following generalization of the well-known Frobenius theorem is proved: Let $G$ be a primitive group of permutations of a set $W=X\cup Y \cup Z$. If $G$ contains a subgroup $H$ which operates trivially on $X$ and primitively on $Y$ and $Z$, and if $|X|\geqslant2$, then $G$ is doubly transitive. Bibliography: 2 titles.
